Random Kriging - 11.1 Definition

In many practical situations, the samples available to estimate a block of ore are not located on a regular grid. The sample sizes and orientations are not constant, and the number and relative position of the samples used for valuation of each block change from block to block. Estimation of a block W might be very complex and time consuming if each sample in the neighbourhood of the block were considered individually. A practical solution consists of grouping the samples in blocks Wi (i = 1, 2, . . . n) in the neighbourhood of W, and estimating µw as a weighted average of the mean xi of the samples in Wi. Possible ways of grouping the samples are illustrated in Fig. 1 1.1. More complex patterns can be found in the literature (Krige, 1966) To calculate the kriging estimator of pw, we must be able to calculate the variance of xi, the covariance of xi and xj, and the covariance of xi and pµw. The purpose of this chapter is to show how these quantities can be calculated when we ignore the position of the samples in the block Wi. We consider the samples to be randomly distributed in Wi; kriging with this assumption is known as random kriging.